Finite Element Analysis

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Did anyone use the Finite Element Analysis for their simulation? Came across this term while reading over the net. Anyone care to explain what is this about? I have trouble understanding it. Thanks.

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OK, in it's simplest sense, FEA is a way of reducing a set of partial differential equations over a given domain (for example: laws governing the motion of fluids, over the space around a wing) into a set of solvable equations. The state variables are only known at certain nodes, and they are interpolated over the inside of the elements. So FEA can be used to simulate anything, as long as you have the equations. However, almost nothing about FEA is fast (in the easiest problems you are still solving large N x N matricies), so if this is for real-time simulation, this is probably not the way to go yet (Game requirements: Cray 6, 32 GB free RAM [8^)

You could use it for games, but the number of elements would have to be pretty small, or worse yet, dynamic, so it could run on all the users' PCs.

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Quote:
 Original post by lonesockOK, in it's simplest sense, FEA is a way of reducing a set of partial differential equations over a given domain (for example: laws governing the motion of fluids, over the space around a wing) into a set of solvable equations. The state variables are only known at certain nodes, and they are interpolated over the inside of the elements. So FEA can be used to simulate anything, as long as you have the equations. However, almost nothing about FEA is fast (in the easiest problems you are still solving large N x N matricies), so if this is for real-time simulation, this is probably not the way to go yet (Game requirements: Cray 6, 32 GB free RAM [8^)You could use it for games, but the number of elements would have to be pretty small, or worse yet, dynamic, so it could run on all the users' PCs.

Thanks for the explanation. No wonder I am not able to find much information on it in the area of computer science/graphics.

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Mystery, may I be bold here & ask what you are working on? It sounds interesting... you have asked some cool questions (FEA, cloth simulation, etc). If its a secret... no biggie

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Actually, the numerical methods coming from the finite elements are VERY similar to those obtained by finite differences. E.g. if you simulate the 1D heat equation, you will get THE SAME method if you use FEA or finite differences! So it's nothing so miraculous at all!

And, Mystery, it is NOT true that you always have to solve an N x N system. This is only the case if you use implicit methods IN TIME (like Backward Euler or Crank-Nicolson), but finite elements is a method for discretization IN SPACE. You can without problems use explicite methods in time and FEA in space. This way, FEA can be quite cheap (especially since it generates sparse matrices). If N is not that big, say 100 or so, real-time simulation might still be feasible.

In my opinion, FEA gives you nothing new (at least I can't think of anything now). You can do everything by finite differences, unless you are interested in error estimators or stuff like that (not very probable for visual simulation though!).

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Quote:
 Original post by Luke MiklosMystery, may I be bold here & ask what you are working on? It sounds interesting... you have asked some cool questions (FEA, cloth simulation, etc). If its a secret... no biggie

Hi Luke

I am working on a project to level/flatten a deformed object down to a plane in hope of restoring some information that are lost because of the deformation. I am still at the very early stages so you can expect me to ask a lot of silly questions. The guys here are really knowledgeable and helpful.

Btw, if you are working on something similar or wishes to discuss, feel free to email/pm me.

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Quote:
 Original post by LutzActually, the numerical methods coming from the finite elements are VERY similar to those obtained by finite differences. E.g. if you simulate the 1D heat equation, you will get THE SAME method if you use FEA or finite differences! So it's nothing so miraculous at all!And, Mystery, it is NOT true that you always have to solve an N x N system. This is only the case if you use implicit methods IN TIME (like Backward Euler or Crank-Nicolson), but finite elements is a method for discretization IN SPACE. You can without problems use explicite methods in time and FEA in space. This way, FEA can be quite cheap (especially since it generates sparse matrices). If N is not that big, say 100 or so, real-time simulation might still be feasible.In my opinion, FEA gives you nothing new (at least I can't think of anything now). You can do everything by finite differences, unless you are interested in error estimators or stuff like that (not very probable for visual simulation though!).

I think I need to solve the problem in TIME rather than space. So the FEA is nothing great afterall. Initially I got the impression FEA can give very accurate results at the expense of high computational cost.

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I have recently came across a microsoft research page dealing with advanced geometry manipulation techniques , including flattening a 3d model to be stored inside a texture. Here's the link

http://research.microsoft.com/%7Ehoppe/

Hope you find it useful.

Ciehoo

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Quote:
 Original post by CiehooI have recently came across a microsoft research page dealing with advanced geometry manipulation techniques , including flattening a 3d model to be stored inside a texture. Here's the linkhttp://research.microsoft.com/%7Ehoppe/Hope you find it useful.Ciehoo

It should be very useful. Thanks. But may I know which article are you referring to? I couldn't find the one you mentioned about flattening of 3D model.

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